$X$ and $Y$ are large,parallel conducting plates close to each other. Each face has an area $A$. $X$ is given a charge $Q$. $Y$ is without any charge. Points $A, B$,and $C$ are as shown in the figure.

$A$ sphere of radius $R$ has a uniform distribution of electric charge in its volume. At a distance $x$ from its centre,for $x < R$,the electric field is directly proportional to

The electric field intensity at a point at a distance $r$ from the axis of an infinitely long pipe having a linear charge density $q$ is proportional to:

$A$ spherical portion has been removed from a solid sphere having a charge distributed uniformly as shown in the figure. The electric field inside the emptied space is $:-$

An electric dipole is placed on the $x$-axis in proximity to a line charge with a linear charge density of $3.0 \times 10^{-6} \, C/m$. The line charge is placed on the $z$-axis. The positive and negative charges of the dipole are at distances of $10 \, mm$ and $12 \, mm$ from the origin,respectively. If a total force of $4 \, N$ is exerted on the dipole,find the magnitude of the positive or negative charge of the dipole.

$A$ charge $Q$ is uniformly distributed over a large square plate of copper. The electric field at a point very close to the centre of the plane is $10 \ V/m$. If the copper plate is replaced by a plastic plate of the same geometrical dimensions and carrying the same charge $Q$ uniformly distributed,then the electric field at the point $P$ will be......$V/m$.